What is the answer to ln(x)-3sqrt(ln(x))+2=0 ?

The answer to ln(x)-3sqrt(ln(x))+2=0 is x=e^4,x=e

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ln(x)-3sqrt(ln(x))+2=0

ln (x) - 3 ln (x) + 2 = 0

x = e^{4}, x = e

Decimal Notation

x = 54.59815 \dots, x = 2.71828 \dots

Solution steps

ln (x) - 3 ln (x) + 2 = 0

Rewrite the equation with

ln (x) = u

u - 3 u + 2 = 0

Solve

u - 3 u + 2 = 0 : u = 4, u = 1

u = 4, u = 1

Substitute back

u = ln (x),

solve for

x

Solve

ln (x) = 4 : x = e^{4}

Solve

ln (x) = 1 : x = e

x = e^{4}, x = e

Verify Solutions:

x = e^{4}

True

, x = e

True

The solutions are

x = e^{4}, x = e

lo g_{3} ((2 x^{2} + 5 x + 4) - 7) = 2

ln (2 x + 4) = ln (x + 3)

lo g_{3} (x + 12) = lo g_{3} (5 x)

lo g_{p} (- 1) = n

lo g_{5} (x - 3) + lo g_{5} (3 x + 1) = 3

What is the answer to ln(x)-3sqrt(ln(x))+2=0 ?
The answer to ln(x)-3sqrt(ln(x))+2=0 is x=e^4,x=e
Solve for x: ln(x)-3sqrt(ln(x))+2=0
The solution is x=e^4,x=e